 16.1: For Exercises 13, sketch the region of integration and evaluatethe ...
 16.2: For Exercises 13, sketch the region of integration and evaluatethe ...
 16.3: For Exercises 13, sketch the region of integration and evaluatethe ...
 16.4: In Exercises 49, sketch the region of integration., 11, 1x21x2f(x, ...
 16.5: In Exercises 49, sketch the region of integration., 20, 04y2f(x, y)...
 16.6: In Exercises 49, sketch the region of integration., 41, yyf(x, y) d...
 16.7: In Exercises 49, sketch the region of integration., 10, sin1 y0f(x,...
 16.8: In Exercises 49, sketch the region of integration., 11, 11, 1z20f(x...
 16.9: In Exercises 49, sketch the region of integration., 10, y0, x0f(x, ...
 16.10: In Exercises 1013, choose coordinates and write a triple integralfo...
 16.11: In Exercises 1013, choose coordinates and write a triple integralfo...
 16.12: In Exercises 1013, choose coordinates and write a triple integralfo...
 16.13: In Exercises 1013, choose coordinates and write a triple integralfo...
 16.14: Write R f(x, y) dA as an iterated integral if R is theregion in Fi...
 16.15: Consider the integral  40 (y4)/20 g(x, y) dx dy.(a) Sketch the re...
 16.16: . Evaluate Rx2 + y2 dA where R is the region in Figure16.60.
 16.17: In Exercises 1723, calculate the integral exactly.. , 100, 0.10xexy...
 16.18: In Exercises 1723, calculate the integral exactly., 10, 43(sin (2 y...
 16.19: In Exercises 1723, calculate the integral exactly., 10, y0(sin3 x)(...
 16.20: In Exercises 1723, calculate the integral exactly., 43, 10x2y cos (...
 16.21: In Exercises 1723, calculate the integral exactly., 10, 1x21x2e(x2+...
 16.22: In Exercises 1723, calculate the integral exactly., 10, z0, 20(y + ...
 16.23: In Exercises 1723, calculate the integral exactly., 10, z0, y0xyz d...
 16.24: Using Cartesian, cylindrical, or spherical coordinates,write an equ...
 16.25: If W is the region in Figure 16.61, what are the limits of integrat...
 16.26: If W is the region in Figure 16.61, what are the limits of integrat...
 16.27: If W is the region in Figure 16.61, what are the limits of integrat...
 16.28: Set up R f dV as an iterated integral in all six possibleorders of...
 16.29: In 2937, decide (without calculating its value)whether the integral...
 16.30: In 2937, decide (without calculating its value)whether the integral...
 16.31: In 2937, decide (without calculating its value)whether the integral...
 16.32: In 2937, decide (without calculating its value)whether the integral...
 16.33: In 2937, decide (without calculating its value)whether the integral...
 16.34: In 2937, decide (without calculating its value)whether the integral...
 16.35: In 2937, decide (without calculating its value)whether the integral...
 16.36: In 2937, decide (without calculating its value)whether the integral...
 16.37: In 2937, decide (without calculating its value)whether the integral...
 16.38: (a) Set up a triple integral giving the volume of the tetrahedronbo...
 16.39: Let B be the solid sphere of radius 1 centered at the origin;let T ...
 16.40: Sketch the region R over which the integration is beingperformed:, ...
 16.41: (a) Convert the following triple integral to spherical coordinates:...
 16.42: In 4245, sketch the region of integration and writea triple integra...
 16.43: In 4245, sketch the region of integration and writea triple integra...
 16.44: In 4245, sketch the region of integration and writea triple integra...
 16.45: In 4245, sketch the region of integration and writea triple integra...
 16.46: In 4650, is the double integral positive or negative,or is it impos...
 16.47: In 4650, is the double integral positive or negative,or is it impos...
 16.48: In 4650, is the double integral positive or negative,or is it impos...
 16.49: In 4650, is the double integral positive or negative,or is it impos...
 16.50: In 4650, is the double integral positive or negative,or is it impos...
 16.51: In 5158, decide (without calculating its value)whether the integral...
 16.52: In 5158, decide (without calculating its value)whether the integral...
 16.53: In 5158, decide (without calculating its value)whether the integral...
 16.54: In 5158, decide (without calculating its value)whether the integral...
 16.55: In 5158, decide (without calculating its value)whether the integral...
 16.56: In 5158, decide (without calculating its value)whether the integral...
 16.57: In 5158, decide (without calculating its value)whether the integral...
 16.58: In 5158, decide (without calculating its value)whether the integral...
 16.59: In 5962, evaluate the integral by changing it tocylindrical or sphe...
 16.60: In 5962, evaluate the integral by changing it tocylindrical or sphe...
 16.61: In 5962, evaluate the integral by changing it tocylindrical or sphe...
 16.62: In 5962, evaluate the integral by changing it tocylindrical or sphe...
 16.63: (a) Sketch the region of integration of, 82, 8y20ex2y2dx dy+, 20, y...
 16.64: A circular lake 10 km in diameter has a circular island2 km in diam...
 16.65: A solid region D is a half cylinder with radius 1 lyinghorizontally...
 16.66: Find the volume of the region bounded by z = x + y,0 x 5, 0 y 5, an...
 16.67: (a) Sketch the region of integration, or describe it preciselyin wo...
 16.68: A thin circular disk of radius 12 cm has density whichincreases lin...
 16.69: Figure 16.62 shows part of a spherical ball of radius 5 cm.Write an...
 16.70: Find the mass of the solid bounded by the xyplane, yzplane,xzplan...
 16.71: Figure 16.63 shows part of a spherical ball of radius 5 cm.Write an...
 16.72: A forest next to a road has the shape in Figure 16.64. Thepopulatio...
 16.73: A solid hemisphere of radius 2 cm has density, ingm/cm3, at each po...
 16.74: Find the volume that remains after a cylindrical hole ofradius R is...
 16.75: Two spheres, one of radius 1, one of radius 2, have centersthat are...
 16.76: For 7677, use the definition of moment of inertiaon page 890.Consid...
 16.77: For 7677, use the definition of moment of inertiaon page 890.Comput...
 16.78: A particle of mass m is placed at the center of one baseof a circul...
 16.79: (a) Find the constant k such that f(x, y) = k(x + y)is a probabilit...
 16.80: Let D be the region inside the triangle with vertices(0, 0), (1, 1)...
 16.81: Let D be the region inside the circle x2 + y2 = 1. Expressthe integ...
 16.82: Compute the iterated integrals , 10, 01x + y(x y)3 dydxand , 01, 10...
 16.83: For each of the following functions, find its average valueover the...
Solutions for Chapter 16: INTEGRATING FUNCTIONS OF SEVERAL VARIABLES
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 16: INTEGRATING FUNCTIONS OF SEVERAL VARIABLES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 16: INTEGRATING FUNCTIONS OF SEVERAL VARIABLES includes 83 full stepbystep solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 83 problems in chapter 16: INTEGRATING FUNCTIONS OF SEVERAL VARIABLES have been answered, more than 43548 students have viewed full stepbystep solutions from this chapter.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Base
See Exponential function, Logarithmic function, nth power of a.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Cone
See Right circular cone.

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Equivalent arrows
Arrows that have the same magnitude and direction.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Inverse cotangent function
The function y = cot1 x

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Perpendicular lines
Two lines that are at right angles to each other

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.

Vertical line
x = a.

Weights
See Weighted mean.